A new heuristic method for solving spatially constrained forest planning problems based on mitigation of infeasibilities radiating outward from a forced choice

Abstract

A new heuristic method to mitigate infeasibilities when a choice is forced into a solution was developed to solve spatially constrained forest planning problems. One unique aspect of the heuristic is the introduction of unchosen decision choices into a solution regardless of the resulting infeasibilities, which are then mitigated by selecting next-best choices for those spatial units that are affected, but in a radiating manner away from the initial choice. As subsequent changes are made to correct the affected spatial units, more infeasibilities may occur, and these are corrected as well in an outward manner from the initial choice. A single iteration of the model may involve a number of changes to the status of the decision variables, making this an n-opt heuristic process. The second unique aspect of the search process is the periodic reversion of the search to a saved (in computer memory) best solution. Tests have shown that the reversion is needed to ensure better solutions are located. This new heuristic produced solutions to spatial problems that are of equal or comparable in quality to traditional integer programming solutions, and solutions that are better than those produced by two other basic heuristics. Three small hypothetical forest examples illustrate the performance of the heuristic against standard versions of threshold accepting and tabu search. In each of the three examples, the variation in solutions generated from random starting points is smaller with the new heuristic, and the difference in solution values between the new heuristic and the other two heuristics is significant (p < 0.05) when using an analysis of variance. However, what remains to be seen is whether the new method can be applied successfully to the broader range of operations research problems in forestry and other fields.

Strategies for regulating timber volume in forest stands

“…Other more modern and robust solution methods may also be found in forest literature, such as the heuristics applied by Bettinger and Zhu (2006), Ghaemi and Feizi-Derakhshi (2014); Gomide et al (2013); Nascimento et al (2012), Pukkala and Heinonen (2006), Silva et al (2009). Non-spatial optimization problems are formulated efficiently by linear programming (HEINONEN, 2007).…”

Forest Planning Heuristics—Current Recommendations and Research Opportunities for s-Metaheuristics

“…In general, some of these processes can be considered repair strategies [8]. One form of repair strategy was employed in the raindrop method designed to address the green-up and adjacency problem in forestry [21,22]. However, other methods have been proposed that may be of value in redirecting a heuristic search away from local optima and toward other …”

“…The ejection chains described in [26] for traveling salesman problems may also be of value to forestry s-metaheuristic search processes. While destruction and reconstruction strategies have been incorporated into one forest planning heuristic [21], direct concrete examples of the potential of these strategies to benefit s-metaheuristics such as tabu search and simulated annealing are lacking at this time. Therefore, as we described in the opening sentence of this section, we see this as an open area for future research endeavors.…”

Tabu Search Experience in Forest Management and Planning

“…Here, the latter of the two provided the better solutions for the planning problems because, as we noted earlier, the addition of a 2-opt process generally improves the quality of the outcomes. Li (2007) recently explored numerous combinations of tabu search, simulated annealing, threshold accepting, and the raindrop method (Bettinger & Zhu 2006) to determine whether a meta-model could be developed that would capitalize on the search behavior of each. The transition between search processes in Li (2007) was determined by continuously assessing the quality of solutions, thus acquiring knowledge of the behavior, then switching heuristic processes when further improvements in solution quality were seemingly lacking.…”